Transcript effort arm >load arm - Lectures For UG-5


Torque is the cross product between a force and the
distance of the force from a fulcrum (the central point about
which the system turns). τ = r × F
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For a lever in mechanical equilibrium, sum of all
the torques acting is zero or the total
anticlockwise moment (torque) is equal to the
total clockwise moment
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M. A. =
Load
Effort
= Effort arm
Load arm
If the effort is farther from the fulcrum than the load
(effort arm >load arm) then the lever is at
mechanical advantage and is a force multiplier.
If the effort is closer to the fulcrum than the load
(load arm> effort arm) then the lever is at
mechanical disadvantage and a speed multiplier.
The muscoskeletal system is designed for speed
and range of motion rather than high force
production
The arrangement of muscles, bones and joints in
the body form lever systems
To figure out which type of lever is formed carefully
look for
 The point of muscle insertion where force is applied
 Locate the joint about which movement is carried
out. It is the fulcrum
 Load or resistance is the part of the body to be
lifted or moved. Its weight acts at its center of
gravity
 Note the force arm and load arm
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When we rise on tiptoe it
is the muscles of the calf
which raise the heel, the
fulcrum is at the toes,
and the weight of the
body falls on the ankle
after the fashion of a
lever of the second
order
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Most levers in the body are third order levers
designed to maximize the speed rather than
maximize the force
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Suppose a person is holding his/her forearm in a horizontal
position with the upper arm vertical
The biceps muscle pulls the arm upwards by muscle contraction
with a force F, the opposing force is the weight of the arm W at
its center of gravity (CG)
The weight of the average person’s forearm (and hand) is about
2% of the total body weight. Say if a person weighs 72kg then the
weight of his forearm is about 1.44kg
Sum of clockwise torques=
Sum of anticlockwise torques
14W=4F
F=14W/4
For W= 15N, F= 52.5 N
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Let’ complicate the problem. Suppose now the
person is holding a ball with weight of 44N
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The force in the biceps is quite
large about twenty six times the
weight of the arm and about
ten times the weight of he ball
For mechanical equilibrium, the
forces must balance. This means
that 383N upward force must be
balanced by the downward
forces
Therefore a 324N downward
force is exerted on the elbow
due to weight of the bone in the
upper arm
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Skeletal muscles typically work at a mechanical
disadvantage so that they must exert a much
greater force than the actual load to be
moved
However lever arrangement enables muscles to
move loads faster over greater distance than
would otherwise be possible
The lower arm can be hold by the biceps muscle at different angles q.
What muscle forces are required for the different arm positions?
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The force developed by biceps is independent of
the angle between the lower and upper arm
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The curvature of deltoid muscle is
important. If the force applied by
the deltoid muscle passed directly
through the fulcrum, there would
be no torque
With the deltoid muscle angled
slightly upward from the horizontal
arm, the direction of the force
does not go through the pivot
point, giving a small nonzero lever
arm
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If the point of insertion of deltoid
muscle is 15cm from the shoulder joint
Weight of the arm is 5% of an average
person’s weight. Say it is 36N and
acting at the center of gravity of the
arm at a distance of 25cm from the
shoulder joint
The force in the deltoid muscle comes
out to be 356N which is about ten
times the weight of the arm. If an
object weighing 10N is held at a
distance of 64cm from the joint the
force in deltoid muscle goes upto
590N
The reason here again is that effort
arm is much smaller than the load
arm
Latissimus dorsi muscle
Gravitational force W applies at the
center of gravity CG of the body.
The center of mass of a body can
be thought as a point about which
the mass of the body is evenly
distributed
 CG
depends on body mass
distribution. Raising the arms over
head lifts CG while bending at hips
and knees lowers it. The higher the
CG less stable a person is
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The
key
to
stable
equilibrium is that the
center of gravity of the
object must be over a
large enough base.
A vertical line through the
center of gravity must fall
within its base of support.
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A person will be in stable equilibrium if he is
standing with his center of gravity lying over the
base formed by his feet. If he spreads his feet
apart then he has a wider base and will be
more stable. If he pulls his feet together he can
be still stable but less so
This works even if the person stands on one foot
but then he has to shift his body such that his
center of gravity is over his feet. He can do this
if he thrusts his hips in one direction and his
shoulders in other direction, changing the
shape of his body and location of his CG
Applied Biomechanics: Concepts and
Connections by John McLester, Peter St.
Pierre
 Bios Instant Notes in Sport and Exercise
Biomechanics by Paul Grimshaw
 Conditioning For Strength And Human
Performance by T. Jeff Chandler, Lee E.
Brown
